Discrete transformations in the Thomson Problem

•A new upper energy limit to the general solution of the Thomson Problem is reported.•Discrete charge transformations yield correspondences with atomic structure.•The transformation is the difference between discrete and continuous charge systems.

A significantly lower upper limit to minimum energy solutions of the electrostatic Thomson Problem is reported. A point charge is introduced to the origin of each N-charge solution. This raises the total energy by N as an upper limit to each (N + 1)-charge solution. Minimization of energy to U(N   + 1) is well fit with −0.5518(3/2)N+1/2 for up to N = 500. The energy distribution due to this displacement exhibits correspondences with shell-filling behavior in atomic systems. This work may aid development of more efficient and innovative numerical search algorithms to obtain N-charge configurations having global energy minima and yield new insights to atomic structure.

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